A cross-linked foamed molded article comprising a polyethylene-based resin has been extensively used as convenience goods, floor covering materials, sound insulating materials, heat insulating materials, footwear members (such as an outer sole, a midsole, an inner sole, and the like), and the like. In particular, as the cross-linked foamed molded article for example, a cross-linked foamed molded article prepared by cross-linking and foaming ethylene-vinyl acetate copolymer is proposed (see, for example, JP-3-2657-B.) In addition, there is proposed a cross-linked foamed molded article which is prepared by cross-linking and foaming an ethylene-α-olefin copolymer which is formed by copolymerizing ethylene and α-olefin using a polymerization catalyst which is formed by contact-treating a co-catalyst carrier formed by a reaction of diethyl zinc, pentafluorophenol, water, silica and hexamethyldisilazane, with a contact-treated matter of triisobutyl aluminum and racemic-ethylenebis(1-indenyl)zirconium diphenoxide [see, for example, JP-2005-314638-A].
When these cross-linked foamed molded articles are used for footwear members such as outer soles, midsoles and inner soles, the cross-linked foamed molded articles are required to have a high fatigue resistance.